The two cats were sighted within about a mile and a half of each other and there's no way to tell if it was two different animals or the same one, according to police.

Officers beefed up patrols in both neighborhoods overnight and stayed in the area today. Officers also notified animal control officers from Palo Alto Animal Services and park rangers from Palo Alto Open Space.

Generally, mountain lions are calm, quiet and elusive, according to an information page on the City of Palo Alto website. They are most commonly found in areas with plentiful prey and adequate cover - conditions that exist in mountain subdivisions, urban fringes and open spaces.

As a result, the number of mountain lion sightings has increased.

If a person sees a mountain lion, the first rule is not to approach the animal, the city said.

"Most mountain lions will try to avoid a confrontation. Give them a way to escape," according to the city.

Also, the city advises residents not to run from mountain lions, because this might set off the animal's instinct to chase.